The Virginia Plan, written by James Madison and proposed by Edmund Randolph (the governor of Virginia) presented a strong central government divided into three branches: executive, legislative, and judicial. The Virginia Plan gave the colonies representation in the government based on population, which worked in favor of the larger states (like Virginia). Madison's plan became the basis of the new United States Constitution and convinced the delegates not to spend time revising the Articles of Confederation, but instead to start over with a whole new form of government.
The small states were worried that they wouldn't have enough say in the government under the Virginia Plan, so they proposed the New Jersey Plan. Under this idea, each state would have the same number of representatives, regardless of its population.
The Great Compromise, also called the Connecticut Compromise, was first suggested by Benjamin Franklin to resolve the differences between the large states' Virginia Plan (representation based on population) and the small states' New Jersey Plan (equal representation regardless of size or population).
Connecticut's representatives, following Franklin's suggestion, proposed that:
Congress consist of two houses: Senate and House of Representatives
House of Representatives be elected on the basis of population (proportional representation) and would have the power to initially propose all bills/laws for taxation and budget (any money collected or spent by the government)
Senate would be elected on the basis of equal representation. In the original proposal the Senate could only accept or reject the bills proposed by the House of Representatives. Now the Senate can amend or change a bill that is proposed by the House of Representatives.
The conflict over slavery was complicated. Slavery had existed in some form throughout the history of the world for thousands of years. Although many of the Founding Fathers / Framers of the Constitution were personally against slavery, all of the citizens attending the Constitutional Convention realized that the large farms & plantations needed slaves to keep operating. The northern states wanted to end slavery, whereas the southern states saw slaves as necessary and important. The issue was whether or not slaves should be counted in a state's population...
The southern states wanted to count the slaves as population for representation. The northern states didn't want the slaves to count if they had no rights as citizens. They thought this would give the South an unfair advantage in votes taken in the House of Representatives. Finally the two sides reached a compromise. The slaves would count as 3/5 of a person for representation to the House of Representatives.